Electrokinetics of spherical colloidal particles with a slip surface in a concentrated suspension

A theory is developed of the electrophoresis of a spherical colloidal particle with a slip surface in a concentrated suspension on the basis of Kuwabara’s cell model. We introduce the slipping length on the particle surface, which is the measure of the particle surface hydrophobicity. We derive the general expression of the particle electrophoretic mobility and its approximate analytic expressions for a particle carrying a low zeta potential. Expressions for other electrokinetics, that is, electrical conductivity, sedimentation velocity, and potential in concentrated suspensions, are also derived. Furthermore, it is shown that as in the case of a dilute suspension, a similarity is found between the electrokinetics of charged spherical solid particles with a slip surface in a concentrated suspension and that for liquid drops. Graphical abstract Electrophoretic mobility of a sphere with a slip surface in a concentrated suspension